Erdös Unit Fractions 

A unit fraction has the form ${\frac{{1}}{{k}}}$ where k is a positive integer.

In 1800 B.C., egyptian mathematicians represented rational numbers between 0 (exclusive) and 1 (inclusive) as finite sums of the form

$${\frac{{1}}{{k_1}}}$$ + ... + $${\frac{{1}}{{k_n}}}$$,

where all the denominators were distinct positive integers.

In 1948 A.C., Paul Erdos and Ernst G. Straus formulated the following conjecture about the unit fractions: for all positive integer n $\geq$ 2 , the rational fraction 4/n can be expressed as the sum of three unit fractions. In other words, it is believed that for each n greater than 1 , there exist positive integers x , y and z such that

$${\frac{{4}}{{n}}}$$ = $${\frac{{1}}{{x}}}$$ + $${\frac{{1}}{{y}}}$$ + $${\frac{{1}}{{z}}}$$

The conjecture has been tested for all n < 10¹⁴ . It remains unknown if the conjecture is a theorem or not.

Given an integer n $\geq$ 2 , your job is to find three positive integers x, y, z whose values verify the Erdos-Straus conjecture.

Input 

The problem input consists of several cases, each one defined in a line that contains an integer number n such that ( 2 $\leq$ n < 10⁴ ).

A line with n = 0 indicates the end of the input.

Output 

For each case in the input, you must print a line with numbers x , y and z (separated by spaces) such that ${\frac{{4}}{{n}}}$ = ${\frac{{1}}{{x}}}$ + ${\frac{{1}}{{y}}}$ + ${\frac{{1}}{{z}}}$ and 0 < x, y, z < 10¹⁶ .

You can print any solution. It's guaranteed that every case in the input has a solution such that 0 < x, y, z < 10¹⁶ .

Sample Input 

10
2
7
0

Sample Output 

5 6 30
1 2 2
4 4 14